Yes, permanent magnets become weaker over time, because it is more energetically favorable for a ferromagnet  to be subdivided into many domains giving a net magnetization of zero.  The timescale of this process will depend on the operating temperature, and whether you can observe this effect in your lifetime is another question altogether.

When a ferromagnetic material is cooled below its Curie temperature, electron spins spontaneously align forming a net magnetization.  However, instead of all the spins facing one direction, the natural configuration consists of many domains such that the aggregate magnetization is zero:

This domain structure has an energy cost of forming domain walls, because it is energetically favorable for every electron to align the same direction of their neighbor.  However, the reduction of magnetostatic energy, which would be large if you had a net magnetization, makes up for the cost of forming domain walls.

Now, a permanent magnet with a net magnetization of zero is rather useless, so when permanent magnets are manufactured, they are subjected to a large magnetic field to align all the domains.  Furthermore, impurities can be employed to 'pin' the magnetic structure, such that if a small domain of the opposite magnetization does form, it is difficult for it to grow larger.

It depends on heat and the presence of other magnets.  This is a problem with computer tape in archival storage.  Because it is stored in rolls, the magnetic fields in the layers will try to imprint themselves on other layers, effectively erasing themselves.  With heat this problem accelerates.

In the magnetic configuration on the right, there is small but finite probability for any one of the spins spontaneously flipping.  The higher the operating temperature relative to the Curie temperature, the higher the likelihood of this process.  When one spin flips, if it doesn't immediately flip back, its neighbor is more likely to flip as well, and a small domain of opposite magnetization can grow.  The growth of this domain will probably be limited by pinning sites which are intentionally introduced into the material to inhibit this very process.  But nevertheless, small domains of opposite magnetization will form, especially around the edges, and the magnet will become slightly weaker over time.  However, you will have to wait a very long time for it to completely demagnetize.

It depends on the type of magnet.  Yes, within a detectable amount of time ceramic and alnico magnets will lose their strength.  The neodymium Iron Boron magnets have the strongest resistance to demagnetization of any magnet material and it is generally estimated that it may take over 500 years before they start to see noticeable  loss of magnetic strength.